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%I #9 Jun 30 2022 08:36:36
%S 1,2,3,5,7,9,11,13,15,17,19,21,23,25,26,27,29,31,33,34,35,37,38,41,45,
%T 46,47,49,51,53,57,59,61,62,65,67,69,71,73,77,78,81,83,85,89,91,93,95,
%U 97,98,99,101,103,105,107,109,111,113,115,118,121,122,123,125
%N Numbers k such that A020696(2^k-1) < A020696(2^k+1).
%C Sándor (2021) showed that all the Mersenne exponents (A000043) are in this sequence and conjectured that both this sequence and its complement are infinite.
%H József Sándor, <a href="https://nntdm.net/volume-27-2021/number-3/29-38/">On Vandiver's arithmetical function - I</a>, Notes on Number Theory and Discrete Mathematics, Vol. 27, No. 3 (2021), pp. 29-38.
%e 2 is a term since A020696(2^2-1) = A020696(3) = 8 and A020696(2^2+1) = A020696(5) = 12 > 8.
%t v[n_] := Times @@ (Divisors[n] + 1); Select[Range[150], v[2^# - 1] < v[2^# + 1] &]
%o (PARI) f(n) = my(d = divisors(n)); prod(i=1, #d, d[i]+1); \\ A020696
%o isok(k) = f(2^k-1) < f(2^k+1); \\ _Michel Marcus_, Jun 30 2022
%Y Cf. A000043, A000668, A020696.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jun 29 2022
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